Use the image to answer the question.

Question

Triangle A B C is drawn with a solid line and is located in quadrant 2 of a coordinate plane. Triangle E F G is drawn with a dotted line and is located in quadrant 1. Angle A and Angle E are labeled as equivalent angles measuring 45 degrees.

Answer these two questions in 3–5 sentences. Are the figures similar? ΔABC has vertices A(−4,3) , B(−3,1) , and C(−1,2) . ΔABC is rotated clockwise about the origin and then translated. ΔEFG has vertices E(4.5,5) , F(1.6,3.8) , and G(3,1.5) . Is ΔEFG the image of ΔABC ?

Answer 1

To determine if triangles ΔABC and ΔEFG are similar, we first examine the angles and the corresponding vertices. Since angles A and E are both 45 degrees, we can consider that they share one corresponding angle. However, similarity requires that all corresponding angles be equal and that the ratios of corresponding sides be constant.

Now, to assess if ΔEFG is the image of ΔABC after a rotation and a translation, we can analyze the coordinates of the vertices. The rotation and translation would maintain the properties of length and angle measurement, but upon examining the vertices, the coordinates suggest that the shapes and orientations do not match. Additionally, since the triangles are in different quadrants and given the need for a specific rotation and translation, it is unlikely that ΔEFG is the direct image of ΔABC. Thus, while the angles may suggest a potential similarity, the overall transformation and position indicate otherwise.